All the Codeword Symbols in Polar Codes Have the Same SER Under the SC Decoder
All the Codeword Symbols in Polar Codes Have the Same SER Under the SC Decoder
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DOI：
10.1109/tcomm.2023.3265687
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发表时间：
2022-03
影响因子：
8.3
通讯作者：
Guodong Li;Min Ye;Sihuang Hu
中科院分区：
文献类型：
--
作者：
Guodong Li;Min Ye;Sihuang Hu
Let ${\mathbb F}_{p}$ be a prime field and let $\mathbb {F}_{q}$ be a larger finite field obtained from adjoining an element $\alpha $ to ${\mathbb F}_{p}$ , i.e., $\mathbb {F}_{q}= {\mathbb F}_{p}(\alpha)$ . We consider polar codes constructed from the $2\times 2$ kernel $\begin{aligned} \begin{bmatrix} 1 & 0 \\ \alpha & 1 \end{bmatrix} \end{aligned}$ over $\mathbb {F}_{q}$ . We prove that for any $\mathbb {F}_{q}$ -symmetric memoryless channel, any code length, and any code dimension, all the codeword symbols in such polar codes have the same symbol error rate (SER) under the successive cancellation (SC) decoder.
Let ${\mathbb F}_{p}$ be a prime field and let $\mathbb {F}_{q}$ be a larger finite field obtained from adjoining an element $\alpha $ to ${\mathbb F}_{p}$ , i.e., $\mathbb {F}_{q}= {\mathbb F}_{p}(\alpha)$ . We consider polar codes constructed from the $2\times 2$ kernel $\begin{aligned} \begin{bmatrix} 1 & 0 \\ \alpha & 1 \end{bmatrix} \end{aligned}$ over $\mathbb {F}_{q}$ . We prove that for any $\mathbb {F}_{q}$ -symmetric memoryless channel, any code length, and any code dimension, all the codeword symbols in such polar codes have the same symbol error rate (SER) under the successive cancellation (SC) decoder.